Abstract
We introduce a new fragment GF 2 + \( \overrightarrow {TG} \) of the first order logic — the two-variable guarded fragment with one-way transitive guards. This logic corresponds in a natural way to temporal logics without past operators. We prove that the satisfiability problem for GF+\( \overrightarrow {TG} \) is EXPSPACE-complete. The lower bound, obtained for the monadic version of the considered logic without equality, improves NEXPTIME lower bound for the whole two-variable guarded fragment with transitive guards GF 2 + TG, given by Szwast and Tendera [8].
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References
H. Andréka, J. van Benthem, I. Németi, Modal Languages and Bounded Fragments of Predicate Logic, ILLC Research Report, 1996.Journal ver.: J. Philos. Logic, 27 (1998), No.3, 217–274.
J. Balcázar, J. Diaz, J. Gabarró, Structural Complexity II, Springer 1990.
A. Chandra, D. Kozen, L. Stockmeyer, Alternation, JACM, 28, No.1 (1981), pages 114–133.
H. Ganzinger, C. Meyer, M. Veanes The Two-Variable Guarded Fragment with Transitive Relations, Proc. of 14-th IEEE Symp. on Logic in Computer Science, pages 24–34, 1999.
E. Grädel, On the restraining power of guards, Journal of Symbolic Logic 64:1719–1742, 1999.
E. Grädel, P. Kolaitis, M. Vardi, On the decision problem for two-variable first order logic, Bull. of Symbolic Logic, 3(1):53–96, 1997.
E. Grädel, I. Walukiewicz, Guarded Fixpoint Logic, Proc. of 14th IEEE Symp. on Logic in Computer Science, pages 45–54, 1999.
W. Szwast, L. Tendera On the decision problem for the guarded fragment with transitivity, Proc. of 16-th IEEE Symp. on Logic in Computer Science, pages 147–156, 2001.
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Kieroński, E. (2002). EXPSPACE-Complete Variant of Guarded Fragment with Transitivity. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_50
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DOI: https://doi.org/10.1007/3-540-45841-7_50
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